JP2016126776A - Simulating machining of workpiece - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an improved method and system for simulating machining of a workpiece.SOLUTION: There is provided a computer-implemented method for simulating the machining of a workpiece with a cutting tool having at least one cutting part and at least one non-cutting part. The method comprises providing a set of dexels that represents the workpiece, a trajectory of the cutting tool, and a set of meshes each representing an individual cutting part or non-cutting part of the cutting tool (S10). The method also comprises, for each dexel, computing, for each mesh, the extremity points of all polylines that describe a time (h,t) diagram (S20), and testing a collision of the cutting tool with the workpiece along the dexel on the basis of the lower envelope of the set of all polylines (S30).SELECTED DRAWING: Figure 4

Description

  The present invention relates to the field of computer programs and systems, and more particularly to methods, systems, and programs for simulating machining of workpieces.

  There are several systems and programs available on the market for object design, engineering, and manufacturing. CAD is an acronym for computer-aided design and relates to software solutions for designing objects, for example. CAE is an acronym for computer-aided engineering, for example, software solutions for simulating the physical behavior of future products. CAM is an acronym for computer-aided manufacturing, for example, relating to software solutions for defining manufacturing processes and operations. In such computer aided design systems, the graphical user interface (GUI) plays an important role in terms of the efficiency of the technique. These techniques can be embedded within a product lifecycle management (PLM) system. PLM helps companies share product data, apply common processes, and leverage company knowledge on product development from product emergence to end of life, across the extended enterprise concept. Refers to business strategy.

  The PLM solution provided by DASSAULT SYSTEMS (under the trademarks CATIA, ENOVIA, and DELMIA) is an engineering hub that organizes product engineering knowledge, a manufacturing hub that manages manufacturing engineering knowledge, and both engineering and manufacturing hubs Provide an enterprise hub that enables enterprise integration and connectivity. All together, the system links products, processes, and resources to enable dynamic knowledge-based product creation and decision support, optimized product definition, manufacturing preparation, production, And bring an open object model to promote services.

  Some systems allow for the representation of a modeled volume using a set of dexels. Some documents specifically suggest using dexel representations for machining simulation or interactive engraving.

  There are examples of such documents (see, for example, Non-Patent Document 1, Non-Patent Document 2, Non-Patent Document 3, Non-Patent Document 4, Non-Patent Document 5, Non-Patent Document 6, Patent Document 1, and Patent Document 2). .

  GPGPU (GENERAL-PURPOSE COMPUTING ON GRAPHICS PROCESSING UNITS) is a graphics processing unit (GPU) that normally processes computations dedicated to computer graphics to perform calculations in applications that are conventionally processed by a central processing unit (CPU). ). Several papers consider using the computational power of current graphics processing units (GPUs) for dexel representation. These papers use the LDNI (LAYERED DEPTH-NORMAL IMAGES) algorithm associated with a specific memory model.

  There are examples of these papers (see, for example, Non-Patent Document 7 and Non-Patent Document 8).

  In general, an algorithm for collision detection describes detection in the case of n dynamic objects, for example. With respect to polygon rendering, many collision detection methods are based on classical geometric objects such as binary space partitioning or Oriented Bounding Volumes. Some algorithms exist for solids represented by CGS. The CGS structure describes a 3D closed solid as a result of a sequence of Boolean operations performed on a single primitive. Eventually, the solid is made by a parametric or implicit equation. This depiction leads to many algorithms for testing intersections between surfaces. These approaches are summarized in several groups, such as analytical methods, lattice methods, tracking methods, implicit equations, etc.

  There are examples of such papers (see, for example, Non-Patent Document 9, Non-Patent Document 10, Non-Patent Document 11, Non-Patent Document 12, and Non-Patent Document 13).

  However, collision detection for NC simulation is special. The specialities of machining simulation can be divided into two. For one thing, the geometry of the workpiece evolves continuously throughout the machining process. The other is that the dynamic tool includes a cutting part and a non-cutting part, for example, a handle (side surface of the tool) and a holding part. In NC machining simulation or more general sculpture simulation configurations, most creators rarely consider checking for collisions between the non-cutting machined part and the unfolding workpiece.

  In the following references (see, for example, Non-Patent Document 14, Non-Patent Document 15, and Non-Patent Document 16), the problem of detecting a collision is described by updating the geometry of the part between each collision test.

  As we have observed, machining simulation has a long history. However, existing solutions are not efficient, especially from the perspective of memory performance, from the perspective of simulation accuracy, and / or from the perspective of user utilization.

  1-3 illustrate the problems that appear when simulating machining a workpiece. In the approach of detecting only the collision at the tool position (refer to Non-Patent Document 17), the collision is detected at each tool position. As a result, what happens when the tool moves from one position to the next is ignored. In order to address such drawbacks, the tool trajectory is always drawn entirely independently so that the distance between two series of tool positions does not exceed a predetermined tolerance. This requires a huge number of checks, and tends to decrease in performance. FIG. 1 shows a false collision between the workpiece 10 and the non-cutting part 12 of the tool 14. FIG. 2 shows the detection of a false collision 20 between the workpiece 10 and the non-cutting part 12 of the tool 14 with a sufficiently discrete arrangement. Such a discrete arrangement is costly (resulting in, for example, a lack of visual fluidity in the simulation) and can never be 100% safe.

  In some approaches, it can be assumed that the workpiece remains stationary means that when handling the machining process, no material transfer event takes place and is impractical. These approaches belong to a more general class of algorithms that detect collisions between two objects that may not progress over time. These algorithms are commonly used to solve path planning problems. In the context of machining simulation, they are used to check that no collisions occur on the designed part.

  A few approaches can deal with the previous two problems. That is, these approaches aim to allow the workpiece to be considered to evolve over time and to detect not only tool position but also collisions along the tool movement. However, these approaches can be based on restrictive assumptions about the tool geometry and discard some tools that require a huge (and infinite) number of protrusions such as bumps can do. These approaches also cannot handle tools characterized by dents or rounds on the tool. More generally, these approaches cannot handle tools that result from Boolean subtraction between protrusions. Approximating such a tool by convex joints actually lacks performance and impairs accuracy. FIG. 3 shows a cutting tool 30 having a non-convex cutting portion 32 that can machine the workpiece 34 without collision with the non-cutting portion 36. As can be seen, the shape of the cutting tool and its trajectory are guaranteed to ensure that the cut always hits the workpiece material first, so that no collision occurs. However, these approaches are prone to accidentally reporting a collision (through performance from other perspectives).

  In this regard, there remains a need for improved solutions for simulating workpiece machining.

US Pat. No. 5,710,709 US Pat. No. 7,747,418

“A VIRTUAL SCULPTING SYSTEM BASED ON TRIPPLE DEXEL MODELS WITH HAPTICS”, XIAOBO PENG AND WEIHAN ZHANG, COMPUTER-AIED DESIGN9 AND APPLICAT “NC MILLING ERROR ASSESSMENT AND TOOL PATH COLLECTION”, YUNCHING HUANG AND JAMES H. OLIVER, PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON COMPUTER GRAPHICS AND INTERACTIVE TECHNIQUES, 1994 "ONLINE SCULPTING AND VISUALIZATION OF MULTI-DEXEL VOLUMES", HEINRICH MULLER, TOBIAS SURMANN, MARC STAUTNER, FRANK ALBERSMANN, KLAUS WEINERT, SM '03 PROCEEDINGS OF THE EIGHTH ACM SYMPOSIUM ON SOLID MODELING AND APPLICATIONS “VIRTUAL PROTOTYPING AND MANUFACTURING PLANING BY USING TRI-DEX MODELS AND HATTIC FORCE FEEDBACK”, YONGFU REN, SUSANA K. LAI-YUEN AND YUAN-SHIN LEE, VIRTUAL AND PHYSICAL PROTOTYPING, 2006 “SIMULATION OF NC MACHINEING BASED ON THE DEXEL MODEL: A CRITICAL ANALYSIS”, SABINE STIFFER, THE INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING 19 “REAL TIME SIMULATION AND VISUALIZATION OF NC MILLING PROCESSES FOR INHOMOGENEOUS MATERIALS ON LOW-END GRAPHICS HARDWARE”, KONIG, A. N. AND GROLLER, E.E. , COMPUTER GRAPHICS INTERNIONAL, 1998. PROCEEDINGS “GPGPU-BASED MATERIAL REMOVAL SIMULATION AND CUTTING FORCE ESTIMATION”, B. TUKORA AND T. SZALAY, CCP: 94: PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY "LAYERED DEPTH-NORMAL IMAGES: A SPARSE IMPLICIT REPRESENTATION OF SOLID MODELS", CHARLIE C. L. WANG AND YONG CHEN, PROCEEDINGS OF ASME INTERNATIONAL DESIGN ENGINEERING TECHNICICAL CONFERENCES BROOKLYN (NY) “Collision detection between geometric models: A survey”, Lin, M .; andGottschalk, S.A. Proc. ofIMA Conference on Mathematicas of Surfaces, 1998; “Improvement of collation-detection algorithm based on OBB”, Journal of Huazhong University of Science and Technology, Zhang Qing, Hang Qing, “Collision detection and analysis in aphysically based on simulation”, W.M. Bouuma and G.M. Vaneck, Proceedings Europeans workshop on simulation and simulation, 1991; “A new collation” detection method for CGS-represented objects in virtual manufacturing, 19 s er s er, s s e s e s e n e u s e, s e s e s e n e, s e s e e, e n e u e, e e “Geometric and Solid Modeling”; M.M. Hoffmann, Morgan KAUfmann, San Mateo, California, 1989 “PRECISE GLOBAL COLLECTION DETECTION IN MULTI-AXIS NC-MACHINGING”, OLEG ILUSHINA, GERSHON ELBERB, DAN HALPERIN, RON WEIN, MYUNG-SO19 “THE SWEEP PLANE ALGORITHM FOR GLOBAL COLLISION DETECTION WITH WORKPIECE GEOMETRY UPDATE FOR FIVE-AXIS NC MACHING”, T. D. TANG, ERIK I.I. , J. et al. BOHEZ, PISUT KOOMSAP, COMPUTER-AIED DESIGN 39 (2007) 1012-1024 “Commercial software CAMWorks (regulated trade mark)” “Precise global collation detection in multi-axis NC-matching”, Oleg Illusima, Gerson Elberb, Dan Halperin, Ron Wein, Myung-SooKim9 Swept Volumes, M.M. Peternell, H.C. Pottmann, T.W. Steiner, H.C. Zhao, Computer-Aided Design & Applications, Vol. 2, no. 5, 2005, 599-608 pages Mathematical Analysis and Numeric Methods for Science and Technology, page 229 Adaptive Precision Floating-Point Arithmetic and Fast Robust Predictates for Computational Geometry

  The present invention provides an improved method, system, and program for simulating machining of a workpiece.

  According to one aspect, therefore, a computer-implemented method for simulating machining of a workpiece using a cutting tool having at least one blade and at least one non-blade is provided. The method is a set of dexels representing a workpiece, each dexel being a set of dexels, including a set of at least one line segment representing an intersection between a straight line and the workpiece, and a trajectory of a cutting tool. Providing a trajectory of the cutting tool that is rigid body motion and a set of meshes, each of which represents a respective blade or non-blade of the cutting tool. Next, the method calculates for each dexel, for each mesh, the end points of all polylines that describe the time of intersection between the dexel line and the mesh as a function of intersection height, according to the cutting tool trajectory. Including the steps of: The method includes testing the cutting tool for collision with the workpiece along the dexel. The step of testing is for a height value corresponding to a position belonging to the lower envelope of the set of all polylines of all meshes, if the polyline to which that position belongs is associated with a non-blade Determining whether it belongs to the dexel line segment.

The method includes one or more of the following.
-The step of calculating the endpoints of all polylines is the intersection of that of the dexel line with each mesh, and for each endpoint of each polyline, based on all the facets of the mesh associated with each polyline. Based on the intersection between the step of determining the volume interface swept by the mesh segment according to the cutting tool trajectory corresponding to the endpoint and the dexel straight line and the determined interface segment Calculating the height, and
The step of calculating the endpoints of all the polylines is for each mesh, determining the visible part of the mesh, where the visible part is the part of the mesh directed towards the trajectory of the cutting tool And calculating the boundary of the volume swept by the visible part according to the trajectory of the cutting tool, and then, for each end of each polyline, the face of the mesh whose intersection with that of the dexel line corresponds to the end Repeating the steps of determining the boundary portion of the volume swept by the minute and calculating the time and height, wherein the step of determining the boundary portion comprises the step of determining the volume of the volume swept by the visible portion Further comprising the step of identifying each boundary portion of the calculated boundary,
The step of calculating the endpoints of all polylines is the step of determining adjacency information about the volume swept by the surface area of the visible part for each mesh, for each polyline, with that of the dexel line The step of determining the boundary portion of the volume swept by the mesh portion, whose intersection corresponds to the first endpoint of the polyline, is to calculate the calculated boundary of the volume swept by the visible portion by geometric calculation. The first surface segment is intersected by a dexel straight line, and the intersection of the dexel straight line with that of the dexel straight line corresponds to the second end point of the polyline. The step of determining the boundary area of the measured volume is swept by the visible part by topological propagation based on adjacency information Further comprising the step of determining a second surface segment of the calculated boundary of the volume, wherein the second surface segment is intersected by a dexel straight line, and / or Is parallelized over a set of
The step of determining the first area performs rasterization over the set of dexels;

  A data structure comprising simulation details of a machining of a workpiece using a cutting tool having at least one blade and at least one non-blade according to the method of the present invention (eg, stored in a file) Proposed.

  Further proposed is a system comprising a processor coupled to a memory storing instructions for performing the method. The processor is a massively parallel processing unit. The system comprises at least one GUI suitable for initiating execution of instructions. The GUI includes a GPU, and the processor is a GPU.

  Further proposed is a computer program comprising instructions for performing the method described above.

  Further proposed is a computer-readable storage medium recording the above-described computer program.

  A method for producing / manufacturing the product is further proposed. The production method includes a simulation phase in which the above-described method for simulating machining is repeated, and then a machining phase for the workpiece.

Embodiments of the invention will now be described using non-limiting examples and with reference to the accompanying drawings.
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  Referring to FIG. 4, a computer-implemented method for simulating machining of a workpiece using a cutting tool is provided. The cutting tool contemplated by the method includes at least one blade and at least one non-blade (also referred to as a “collision” such that the cutting tool is a potentially-somewhat-colliding object) Have The method includes a step S10 of providing a set of dexels that represent the workpiece (in 3D) (the set of dexels and / or the workpiece is also referred to as “modeled volume / object” in the following). By definition, each dexel includes a set of at least one line segment representing an intersection between a straight line and a workpiece (eg, a volume occupied by the workpiece). Here, the dexel corresponds to the position on the straight line where the material of the workpiece exists (that is, the dexel line segment). However, the term “dexel” is alternatively associated with all straight lines of such a 3D model, such that some dexels are deprived of any material / line, eg, from the beginning or by method. Note that it refers to the data. This is simply a matter of definition. The data provided in S10 is the cutting tool (or the trajectory is a plane, eg, a series of positions in the plane, eg, a 2.5 axis trajectory, but in 3D, eg, non-planar). Also included). In the case of the method of the invention, the trajectory of the cutting tool is a rigid body motion (generalization to a more complex trajectory consisting of a series of rigid body motions and a generalization to repeat the method for each series of rigid body motions. Not disturb). The data provided in S10 also includes a set of meshes. Each mesh represents a respective blade or non-blade of the cutting tool (thus, a set of meshes represents a cutting tool). Next, the method includes specific (eg, parallel) processing for each dexel (eg, using a GPU). This includes, for each mesh (e.g., the method loops over the set of meshes), calculating step S20 of all polyline endpoints, where the polyline is a dexel line and mesh (ie, mesh area-or edge). Step S20 is described and calculated as a function of the height of the intersection with the cutting tool trajectory provided in S10. This is followed by step S30 of testing the collision of the cutting tool (e.g., cutting tool sweep) with the workpiece along the dexel (i.e., as the cutting tool blades update / change the dexel). Taking into account the change, the non-blade of the cutting tool—at least responds to the question of whether it collides with at least one material line of the dexel—for example, intersects at some point in time). In particular, for the height value corresponding to the position belonging to the lower envelope of the set consisting of all polylines of all meshes, the step to test is the height if the polyline to which that position belongs is associated with a non-blade. Includes a step of determining whether the value of belongs to the dexel line segment (thus testing whether such a value of height exists). Such a method improves the machining simulation of the workpiece.

  In particular, the method of the invention relates to a simulation of machining a workpiece using a cutting tool having at least one blade and at least one non-blade, where the cutting tool follows a trajectory (the method is a distance relative time). -Any speed, not interested in the speed at which the trajectory is traversed, e.g. any constant speed is contemplated in the calculation), the method may be a cutting tool (more specifically a non-cutting tool). A collision of the blade portion, and hence the collision portion, with the workpiece is detected (S20 and S30). Thus, the method allows a good simulation of industrial machining.

  Furthermore, the method is based on a dexel representation, so it is light in terms of buffering and computation (since dexels allow a discrete and massively parallelizable representation). As a result, the method is flowy / smooth and is therefore responsive, which is highly appreciated at the user end. If the method additionally displays the representation of the workpiece and the representation of the cutting tool that follows the trajectory, for example, perfectly together with the representation of the machining, such a representation is relatively flowing / smooth. And not intermittent. This time, the method further performs tests at S30 based on specific data, ie those calculated at S20, and in particular, the method follows the cutting tool trajectory between the dexel straight line and the mesh. Compute the endpoints of all polylines that describe the time of intersection as a function of intersection height. Again, these data are discrete and the structure of the data contemplated in S20 ensures that the computation is parallelized across dexels. Thus, the method is even more efficient in terms of computation, responsiveness, and memory buffering.

  Furthermore, the calculated data has a specific meaning and they are proposed by the method in S30 (with the previously mentioned prior art time step-based methods that can be regarded as a discrete approach). In contrast, it has certain mathematical properties that allow certain easy and comprehensive tests (in terms of time, as a continuous function). In practice, the method is equivalent to determining geometric conditions once the problem has been successfully written, which causes the method to output the correct result and thus a realistic and correct simulation. These mathematical properties are detailed later. At the present stage, the method can handle relatively arbitrary tools to work well even for non-convex cutting tools and / or cutting tools with non-convex cutting edges (ie Note that the simulation is correct, eg, more collisions are reported correctly and / or fewer collisions are reported incorrectly). The cutting tool is not constrained to be a rotating body (although of course it can be). The cutting tool is, for example, characterized by a void or is a roundover tool. More generally, the cutting tool has a shape resulting from a Boolean subtraction between the convex portions. For example, the method works well with a fairly good animation speed in the situation of FIG. 3 (ie, collisions are not reported incorrectly). The cutting tool is, in the example, a corner rounding end mill, a quarter round tool, a set of milling cutters, or a combination milling cutter. The mathematics behind the method also makes it work relatively well for any (series) of rigid body movements, so that the method is not relatively limited with respect to the tool path.

  Thus, the method of the present invention is robust, fluid / smooth and comprehensive when the tool representation is relatively arbitrary and / or when the workpiece change is relatively arbitrary. The method deals with collision detection during tool movement.

  The method of the present invention is computer implemented. The steps of the method are actually performed in the computer system, by the computer system alone, or by graphical user interaction (ie, the user interacts with the computer system GUI). Thus, steps that are explicitly performed by the computer system are performed completely automatically. In the example, at least some of the triggering of the method steps is performed through a user-computer interaction. In particular, the providing step S10 is executed by a user interaction in which the user specifies the data provided in S10. S10 actually corresponds to the user starting the machining simulation. The calculating step S20 and the testing step S30 are then automatically executed. The level of user-computer interaction required depends on the level of automation that is foreseen and balanced with what is needed to implement the user's wishes. In the example, this level is user defined and / or predetermined.

  A typical example of a computer implementation of the method is to perform the method using a system adapted for this purpose. The system comprises a processor coupled to a memory and a graphical user interface (GUI), the memory recording a computer program containing instructions for performing the method. The memory also stores a database. A memory is any hardware that is adapted for such storage and possibly comprises several physical discrete parts (eg, one for programs and possibly one for databases). The GUI includes a GPU. In such a case, the processor is a GPU. In other words, the processor that performs at least the steps of the method, in particular the calculating step S20 and / or the testing step S30, is a GPU. Such a system is an efficient tool for simulating machining. This is especially true when the workpiece is represented as a collection of dexels. Since dexel-based algorithms are well suited for massively parallel hardware, it is efficient to consider using the computing power of modern graphics processing units (GPUs).

  The method of the present invention generally operates on a modeled object. A modeled object is any object defined by data stored in a database. In a broad sense, the expression “modeled object” also refers to the data itself. The method of the present invention defines a modeled object (e.g., a workpiece), e.g., firstly a workpiece (and thus a 3D modeled object), and then simulates machining of the workpiece by the method. Is part of the process for designing. “Designing a 3D modeled object” refers to any action or series of actions that is at least part of the process of elaborately creating a 3D modeled object. Thus, the method includes creating a 3D modeled object from scratch. Alternatively, the method of the present invention comprises providing a previously created 3D modeled object and then modifying the 3D modeled object, in particular by machining simulated by the method. .

  Depending on the type of system, the modeled object is defined by different types of data. The system is actually any combination of CAD, CAE, CAM, PDM, and / or PLM systems. In these different systems, the modeled object is defined by corresponding data. Accordingly, the CAD object, PLM object, PDM object, CAE object, CAM object, CAD data, PLM data, PDM data, CAM data, and CAE data will be described. However, since the modeled object is defined by data corresponding to any combination of these systems, these systems are not exclusive to others. Thus, the system will be both a CAD system and a PLM system, as will be apparent from the definition of such system provided below.

  By CAD system is meant any system adapted to at least design a modeled object based on a graphical representation of the modeled object, such as CATIA. In this case, the data defining the modeled object includes data that allows a representation of the modeled object. A CAD system provides a representation of a CAD modeled object using, for example, edges or lines, and in some cases, using surface segments or surfaces. A straight line, edge, or face is represented in various ways, for example, a non-uniform rational B-spline (NURBS). Specifically, the CAD file contains a specification from which the geometry is generated, which in turn allows a representation to be generated. Modeled object specifications are stored in single or multiple CAD files. The typical size of a file representing a modeled object in a CAD system is in the range of 1 megabyte per part. A modeled object is typically an assembly of thousands of parts.

  In the context of a CAD system, a modeled object is typically a 3D modeled object that represents a product, or in some cases, an assembly of products, for example, a part or assembly of parts. By “3D modeled object” is meant any object modeled with data that allows 3D representation. The 3D representation makes it possible to see the part from all angles. For example, if a 3D modeled object is 3D rendered, it can be manipulated and rotated around any of its axes or around any axis in the screen where the representation is displayed. This specifically excludes 2D icons that are not 3D modeled. The display of the 3D representation facilitates design (ie, statistically speeds up the designer's work). This speeds up the manufacturing process in the industry, as product design is part of the manufacturing or modeling process.

  A 3D modeled object can be a virtual design using, for example, a CAD software solution or CAD system, such as a (eg, machine) part or assembly of parts, or more generally any rigid assembly (eg, a moving mechanism). Represents the geometric shape of the product that is manufactured in the real world. CAD software solutions enable the design of products in a variety of industrial sectors, including aerospace, architecture, construction, consumer goods, high-tech devices, industrial equipment, transportation, maritime and / or offshore, or transportation. 3D modeled objects designed by the method of the present invention are therefore ground vehicle parts (including, for example, automobile and light truck equipment, racing cars, motorcycles, truck and motor equipment, trucks and buses, trains), Aircraft parts (including, for example, airframe equipment, aerospace equipment, propulsion equipment, defense products, aviation equipment, space equipment), ships (including, for example, naval equipment, merchant ships, offshore equipment, yachts and work ships, marine equipment) Machine parts (including, for example, industrial manufacturing machines, mobile heavy machinery or equipment, installation equipment, industrial equipment products, processed metal products, tire manufacturing products), (eg, consumer electronics, security and / or control and (Including instrumentation products, computing and communication equipment, semiconductors, medical devices and equipment) Electronic goods, consumer goods (including, for example, furniture, residential and garden products, leisure goods, fashion products, durable consumer goods products, non-durable consumer goods products), (eg food and beverages and tobacco, beauty and Represents industrial products that are packaging (including personal care and household goods packaging).

  By PLM system is meant any system adapted for the management of modeled objects that represent physical manufactured products. In a PLM system, the modeled object is thus defined by data suitable for the production of a physical object. These are generally dimensional values and / or tolerances. It is actually better to have such a value for the accurate production of the object.

  CAM stands for computer-aided manufacturing. By CAM solution is meant any solution, hardware software, adapted to manage product manufacturing data. Manufacturing data generally includes data relating to the product to be manufactured, the manufacturing process, and the resources required. The CAM solution is used to plan and optimize the entire manufacturing process of the product. For example, it can provide CAM users with information about the number of resources, such as feasibility, duration of the manufacturing process, or a particular robot used in a particular step of the manufacturing process, and thus Allows decisions on management or required investment. CAM is a successor process after the CAD process and potential CAE process. Such a CAM solution is provided by Dassault Systems under the trademark DELMIA®.

  CAE stands for computer aided engineering. By CAE solution is meant any solution, software, or hardware adapted for analysis of the physical behavior of the modeled object. A well-known and widely used CAE technique generally involves dividing a modeled object into elements whose physical behavior can be calculated and simulated through formulas (FEM). It is. Such a CAE solution is provided by Dassault Systems under the trademark SIMULIA®. Another growing CAE technique involves the modeling and analysis of complex systems of components belonging to different fields of physics that do not use CAD geometry data. The CAE solution allows simulation and thus allows optimization, improvement, and verification of the manufactured product. Such a CAE solution is provided by Dassault Systems under the trademark DYMOLA®.

  PDM represents manufacturing data management. By PDM solution is meant any solution, software, or hardware that is adapted to manage all types of data associated with a particular product. PDM solutions are used by all parties involved in the product life cycle, mainly by engineers, but also by project managers, finance personnel, sales personnel, and purchasers. PDM solutions are generally based on product-oriented databases. It allows users to share consistent data about the product and thus prevents parties from using different data. Such a PDM solution is provided by DASSAULT SYSTEMS under the trademark ENOVIA®.

  FIG. 5 shows an example of the GUI of the system, and the system is a CAD system.

  The GUI 2100 is a typical CAD-like interface and has a standard menu bar 2110, 2120, and a bottom tool bar 2140 and a side tool bar 2150. Such menu bars and tool bars include a set of user selectable icons, each icon being associated with one or more operations or functions as is known in the art. Some of these icons are associated with a displayed software tool that is adapted for editing and / or working with the 3D modeled object 2000 displayed in the GUI 2100. For example, the result of executing the method. Software tools are grouped into workbenches. Each workbench includes a subset of software tools. In particular, one workbench is an editing workbench that is suitable for editing the geometric features of the modeled product 2000. In operation, the designer may select a geometric by, for example, preselecting a portion of the object 2000 and then starting the operation (eg, changing dimensions, colors, etc.) or selecting an appropriate icon. Edit the constraints. For example, a typical CAD operation is modeling the drilling or folding of a 3D modeled object displayed on the screen. The GUI displays, for example, data 2500 related to the displayed product 2000. In the example of FIG. 2, data 2500 displayed as a “feature tree” and their 3D representation 2000 relate to a brake assembly including a brake caliper and a brake disc. The GUI can display various types of graphic tools 2130, 2070, 2080, for example, to facilitate 3D orientation of objects, to trigger simulation of edited product behavior, or displayed Further shown for rendering various attributes of product 2000. The cursor 2060 is controlled by the haptic device to allow the user to interact with the graphic tool.

  FIG. 6 shows an example system, which is a client computer system, eg, a user's workstation.

  The example client computer comprises a central processing unit (CPU) 1010 connected to an internal communication bus 1000 and a random access memory (RAM) 1070 also connected to the bus. The client computer is further provided with a graphical processing unit (GPU) 1110 associated with a video random access memory 1100 connected to the bus. Video RAM 1110 is also known in the art as a frame buffer. Mass storage device controller 1020 manages access to mass memory devices, such as hard drive 1030. Large capacity memory devices suitable for tangibly implementing computer program instructions and data include, by way of example, semiconductor memory devices such as EPROM, EEPROM, and flash memory devices, and magnetic disks such as internal hard disks and removable disks, All forms of non-volatile memory including magneto-optical disks and CD-ROM disks 1040 are included. Any of the above may be supplemented by or incorporated into a specially designed ASIC (Application Specific Integrated Circuit). The network adapter 1050 manages access to the network 1060. The client computer also includes a haptic device 1090 such as a cursor control device or keyboard. The cursor control device is used at the client computer to allow the user to selectively position the cursor at any desired location on the display 1080. In addition, the cursor control device allows the user to select various commands and enter control signals. The cursor control device includes a number of signal generation devices for control signals input to the system. Typically, the cursor control device is a mouse and mouse buttons are used to generate signals. Alternatively or additionally, the client computer system comprises a sensitive / touchpad and / or a sensitive / touch screen.

  The computer program includes instructions executable by a computer, and the instructions constitute a means for causing the system described above to perform the method. The program can be recorded on any data storage medium including the memory of the system. The program is implemented, for example, with digital electronic circuitry or with computer hardware, firmware, software, or a combination thereof. The program is implemented as an apparatus, for example, a product that is tangibly implemented in a machine-readable storage device for execution by a programmable processor. Method steps are performed by a programmable processor that executes a program of instructions to perform the functions of the method by manipulating input data and generating output. Accordingly, the processor is programmable and coupled to receive data and instructions from and transmit data and instructions to the data storage system, at least one input device, and at least one output device. The application program is implemented in a high level procedural programming language or object oriented programming language, or in assembly language or machine language if desired. In either case, the language is a compiler language or an interpreter language. The program is a complete installation program or an update program. Application of the program on the system results in instructions for executing the method in any case.

  Further, the method details (ie, the data provided at S10, the data calculated at S20, and the results determined at S30) are all, for example, for later use by a third party, eg, data Note that it is stored in the file. In particular, the simulation is played / redisplayed at any time. The simulation is performed in a product production / manufacturing process that is executed based on a data file, for example. Such a process, as is known, includes a simulation phase in which the machining simulation is repeated, followed by a (real) machining phase for the (real) workpiece based on the simulation results. . For example, in each simulation where a collision is detected, the process repeats the simulation by adjusting the trajectory. The simulation of FIG. 4 allows easy calculation of the impact depth (classical data known to be important in the field of machining), and therefore the trajectory is based on such data. It should be noted here that it can be adjusted efficiently. This can be repeated until no collision is detected and / or until a satisfactory trajectory is determined. Thereafter, actual machining is performed to reproduce the retained simulation trajectory.

  The providing step S10 will now be described.

  The method includes a step S10 of providing a set of dexels that represent the modeled volume (of the workpiece). This allows a light representation of the modeled volume (in other words, the modeled volume is represented using little memory space). This also allows a representation of the modeled volume that is easily processed. In particular, design operations on the modeled volume are performed particularly efficiently (eg, parallelized) thanks to the data structure of the set of dexels, where the modeled volume is represented by the set of dexels. . In other words, this structure enables massively parallel processing. Thus, the design operation is performed with high responsiveness and high robustness.

  For the method of the present invention, the dexel representation is more explicitly relied upon in S20 and S30 to perform a collision test. Thus, the method efficiently combines the computational benefits of dexel representation with the considerations of reality in simulation.

  The term “dexel” is known as a simplified representation of “depth element” (just as the term “pixel” is a simplified representation of “picture element”). The dexel concept is mentioned in many research papers. In the context of the method of the present invention, a dexel includes at least one line segment, ie a set of 3D point pairs. In the example, the modeled volume includes at least one dexel that includes a set of at least two line segments. The dexel line segments may be ordered if there are several (in which case the dexels are a list) or unordered. The dexel line represents the intersection between the straight line and the modeled volume. In other words, when considering a virtual straight line intersecting the modeled volume, a dexel is a set of line segments derived from a given straight line and obtained from the intersection calculation. Thus, the step of providing a set of dexels is such as by following an imaginary line and calculating the intersection with the modeled volume initially represented by B-Rep or any other volume representation. A step of calculating a simple intersection. Thus, the set of dexels represents the modeled volume (ie, the workpiece).

  It is important to note that the set of dexels is provided as computer-implemented data in S10. Thus, for any representation of the modeled volume, the definitions provided above and below have implications from a data structure perspective. For example, a line segment is provided as a pair of 3D positions (eg, two 3D positions tied together), such as a height on a dexel line, and also uses straight line geometry (reference points and directions). Even provided. The 3D position is also provided as a list of three coordinates (eg, floating point numbers) associated with the reference 3D frame. A dexel is a collection of line segments, which implies that the line segments are tied together in a defined structure. The dexels in the set of dexels are similarly tied together. Representing a workpiece by a set of dexels that itself includes a set of at least one line segment allows a fast update step S30 of the workpiece.

  The dexel concept will now be illustrated with reference to FIGS. 7-9, which provides an example of step S10 that provides a set of dexels as a dexel structure 67.

  Given a modeled volume and an infinite line, a dexel is a set of line segments (or sections) representing the intersection between the infinite line and the modeled volume (of the workpiece). This set of line segments is captured in memory as a set of boundary points for each line segment. For example, a reference point / origin (a point with a height of 0-zero) is defined on each line, and the height on that line (eg, an algebraic value, ie, a negative or positive scalar value, eg, sign Generalized integers or real numbers, eg floating point numbers or any other adapted data type, determine boundary points (this framework for defining height applies to S20, eg Note that the origin is used). A dexel structure is a collection of dexels (each containing a set of line segments), eg organized by being ordered on a rectangular grid (eg, sharing the same direction, eg, the entire structure is in that direction Includes three grids, each two orthogonal). 7 and 8 show the modeled volume 40 with a 10 × 10 straight 50 grid. The example method includes providing a modeled volume 40 (representing a workpiece), eg, as a B-Rep, as shown in FIG. Next, the example method includes defining a grid of 10 × 10 straight lines 50 that intersect (at least in part) the modeled volume 40, as shown in FIG. Next, the example method includes calculating a dexel 65 that includes a set of line segments 60 and / or line segments 62, as represented in FIG. In the figure, one dexel 65 is surrounded by a circle. The dexel 65 includes several line segments 60 or one line segment 62 depending on whether the straight line 50 intersects the modeled volume 40 at one location or at several separate locations. Of course, the method or alternatively retrieves the dexel 65 from the memory. In either case, dexel structure 67 is provided in this manner.

  FIG. 9 shows the resulting dexel structure 67. Not all straight lines 50 intersect the modeled volume 40 (in the example, only 52 straight lines intersect the modeled volume 40), producing as many dexels 65 as modeled (modeled). Note that straight lines that do not intersect volume 40 are completely discarded and do not generate dexels). In addition, some straight lines 50 intersect the modeled volume 40 through one line segment 62 (eg, dexel (2,3) or dexel (9,6)), others include several line segments 60. Through, for example, two line segments (eg, dexel (7,7) or dexel (4,7)), or three line segments (dexel (2,8) or dexel (5,8)), or four Crosses the modeled volume 40 through a line segment (Dexel (2, 9) or Dexel (4, 9)). The resulting dexel structure 67 includes 36 dexels 65 with one line 62, six dexels 65 with two line segments 60, five dexels 65 with three line segments 60, and four lines 52 dexels 65 are included, including 5 dexels having minutes 60.

  The set of dexels provided in S10 is a tridexel structure. A tridexel structure is generally defined by including three dexel structures, including a dexel structure parallel to the x-axis, a dexel structure parallel to the y-axis, and a dexel structure parallel to the z-axis. The method includes displaying a graphical representation of the workpiece at any time, for example during the calculating step S20 and the testing step S30. The displaying step is based on a set of dexels. The tridexel structure provides good display because it is almost independent of the “view direction”. The tridexel structure provides a more accurate display, especially when the user changes the viewpoint.

  10-12 show dexel structures that each represent the same modeled volume. In other words, the modeled volume is defined by tridexel data, including the three dexel structures of FIGS. 10-12 (eg, having orthogonal directions). FIG. 10 shows a dexel structure 67 along the y-axis. FIG. 11 shows a dexel structure 68 along the x-axis. FIG. 12 shows a dexel structure 69 along the z-axis. In each figure, the dexel straight line is parallel to the respective axis.

  The principle of machining simulation for the method of the present invention is to calculate the intersection of each dexel with the sweep volume of the tool, and cut the material section accordingly. The present invention at least virtually (1) computes the intersection with the tool blade and non-blade at S20, and (2) at S30, to order these intersections in chronological order. By attaching, it goes one step further. It is then possible to understand whether the blade meets the material before or after the non-blade and reports only actual collisions.

  The data provided in S10 also includes a representation of the cutting tool in the form of a set of meshes (corresponding to the cutting tool geometry). A mesh specifies an arbitrary graph structure with vertices (3D positions) and edges (eg, line segments) that connect the vertices two by two and form the so-called face segment of the mesh (ie, the minimum circulation of edges) To do. The meshes are in particular quadrilateral meshes (mainly or completely consisting of four-sided-convex-face segments) and (mainly or completely consisting of three-sided facets) for fast and simple calculations in S20. One of the different types, such as a convex mesh, including a triangular mesh, eg, a mesh having a convex polygonal surface. In other elaborate examples, the mesh has a more complex structure, such as B-Rep, and the term “mesh” is understood in the most general definition in such cases.

  A tool model (corresponding to a real world tool) is defined by a list of adjacent solids, each solid being a blade or non-blade. In the example, the mesh is a solid triangulated boundary. As a result, the tool is provided at S10 as a list of meshes that do not intersect with the closed self. Each mesh represents a blade portion of the tool or a non-blade portion of the tool. The mesh representing the blade is labeled, for example, “cut” and / or the mesh representing the non-blade is labeled, for example, “collision”. The intersection of the two meshes of the tool has zero volume, i.e. the two meshes are separated or they share a surface segment (or overlap of surface segments) that models the contact area. means. Any tool geometry can be represented in this way by using a boule polyhedron operation. As such, these assumptions do not constrain the generality of the method.

  Also at S10, a cutting tool trajectory is provided. The method is mainly described later for a three-axis trajectory, but can be extended to more complex trajectories (eg, five axes). The trajectory is provided as a polygonal line in a three-dimensional space, and each straight line segment is hereinafter referred to as a “basic trajectory”. The tool moves by translation along the straight line of the three-axis trajectory. Along the straight line of the 5-axis trajectory, the tool moves by translation, and in addition, the tool axis changes linearly from the initial orientation to the final orientation. However, any other method of defining the trajectory provided in S10 is also contemplated.

The method then includes a specific process for each dexel D of the modeled volume. First, in S20, for each mesh M, the method forms the so-called “(h, t) diagram” of the simulation, and finds all polyline endpoints (hereinafter referred to as L ₁ , L ₂ , L ₃ ). calculate. By definition, a polyline describes a (h, t) position, in other words, based on (e.g., any-e.g. Arbitrary-origin / reference and / or arbitrary-e.g. Arbitrary-scale). Also, the 2D position is described using the abscissa corresponding to the height of the dexel (using, for example, the height definition mentioned above) and the ordinate corresponding to the time. For any dexel given anywhere in the method, any height and / or time scale is implemented as long as the scale is consistent (eg, the same). For easier implementation, the same scale is performed for all dexels. With respect to the height scale, for example, in the case of a tridexel structure, such as one of FIGS. 10-12, the origin of each direction is for all dexels supported by a straight line having the same direction-orthogonal to that line. Defined on the same plane. Not all these data are calculated in S20, and without using any further information (apart from the cutting / collision attribute information), just a set of integer and / or real values (ie Note that it is only necessary to have a comparable (h, t) position (denoted as an ordered pair). Thus, the (h, t) diagram, described in more detail later, must be understood as a mathematical object to which the data processed by the method of the invention is associated, especially even for polylines (especially in S20). The calculated data includes the endpoints of all the polylines in the figure).

  Now, by definition, the polyline describes / represents the time t of intersection between each dexel D line and each mesh according to the trajectory of the cutting tool as a function of the intersection height h (hence Note that a polyline is associated with each mesh in the set of meshes, but one mesh is associated with several respective polylines, depending on the complexity of the trajectory and also the complexity of the mesh. If, for example, the mesh defines a convex volume, it generates a single polyline--for example, on a translation trajectory--but if the mesh does not define a convex volume, for the same trajectory, it connects the visible parts. Note that it produces the same number of polylines as having parts) (as mentioned above, any timing / A speed, for example, a certain time is kept for the trajectory, so that each polyline must be obtained from a connected complete line segment, and the main characteristics of the (h, t) diagram detailed below. Note that the same applies to the more general case anyway). In fact, each mesh is virtually moved according to the trajectory, thereby virtually meeting / intersecting with each dexel's straight line (does not intersect—for example, the mesh never meets a given straight line) (Thus, in practice, it is understood as an empty intersection associated with an empty / zero polyline without loss of generality). The method virtually tracks the height of such encounters over time for all meshes. The method then virtually considers the time of encounter with height (the inverse of the tracked data). However, the method finally calculates only the end points of the polyline in S20.

  Thanks to S20 and (for all meshes) all polyline endpoints, and thanks to the specific nature of the (h, t) diagram, the method then determines whether there is a collision (still in S30). Simply test (for each dexel), which further provides the depth of the collision (the dexel line and the boundary height of the collision on the dexel line) if there is a collision. The step S30 to test, especially for the height value corresponding to the position belonging to the lower envelope of the set of all polylines of all meshes, if the polyline to which the position belongs is associated with a non-blade Determining whether the value of belongs to the dexel line segment (i.e. whether the height value is also included in the material section held in the dexel). (In the (h, t) diagram for a specific orientation, in other words for time, and in other words for projection on the h-axis, for the classical lower envelope of the polyline in (h, t) diagram. By definition, the lower envelope of a set of all polylines of all meshes (defined as the minimum time position of a polyline with respect to height—in other words, a set of (h, t)) was virtually considered. It is again noted here that the testing step is only a mathematical object and that the step of testing does not actually require such an object to be calculated. The lower envelope in the 2D view of the polyline is also a 2D object defined as part of the polyline that can be seen by an observer sitting at (0, -∞) and looking up. Note that the polyline in the (h, t) plane, given by the intersection between the sweep mesh and dexel, is a graph of piecewise linear functions. Thus, the calculation of the lower envelope with respect to time values is only an application of the classical definition. In fact, a point on the dexel line segment / interval (thus corresponding to the workpiece material as opposed to the dexel non-line segment position corresponding to aerial / empty) is cut first (in time). It is only tested whether it is met by a mesh or a collision mesh. This is because once all the endpoints of all polylines are collected and associated with a “cut” or “collision” label / attribute based on the corresponding mesh type (described later) This is easily done using the mathematical expedient provided above (thanks to the characteristics of the (h, t) diagram). In a sense, this is equivalent to projecting the lower envelope of the polyline onto the dexels and determining, for each position of each line segment of the dexel, whether the position labeled with the collision label was the first projection. (If applicable, there is a collision, but it is the opposite—that is, if the cut-labeled position is projected first, or the polyline position is not projected at all- Because there is an encounter with the department and therefore to remove material, or no encounter at all).

  Obviously, once test S30 has been performed, for example, particularly if the conclusion of the test is that there is no collision, the method will determine the position of the intersection with the blade of the cutting tool—ie, the height— ( And updating the set of dexels, for example, by removing the line segment or part thereof according to the time). Such data is actually part of the data determined in S20 and / or S30.

  Thus, the method allows for fast detection of collisions, which can accurately provide even the collision depth (collision magnitude and position) and can be performed via massively parallelization across dexels. it can. Addressing the problem of accurate solutions (providing robust and comprehensive collision detection), in the prior art, probably obtaining a description of all machining steps (from a computational point of view) Note that it has not been implemented (although machining simulation has already been studied for many years) because it was considered too complex. Basically, continuity problems are of course avoided due to the unlimited complexity that computer-implemented solutions present theoretically. However, the method arrives at an accurate solution by discretizing the problem (based on test S30, the endpoint computed in S20, and hence the discretized set of inputs). However, discretization is performed on dexels rather than on time (as in prior art time series methods), which leads to a more realistic solution. This is done by taking advantage of certain characteristics of the underlying figure that supports the endpoints. This will be described in detail later. Furthermore, this representation is more suitable for massively parallel computing and allows good performance even in the case of elaborate work discretization.

  In an example, the method utilizes the trajectory provided in S10 to calculate the sweep volume (eg, by sweeping the triangulated boundary of the volume) and / or the sweep surface (within S20). . There are typical references (see, for example, Non-Patent Document 18). This concept is described in detail below.

  A subset of 3D space

Give a point

The notation M + P is a translation of the set M to P. To be precise, M + P = {x + P, xεM}.

  Give a mesh M, which is the starting point and ending point of the basic trajectory, respectively

Is given, the sweep S (M) of the mesh M along the basic trajectory is

Defined by

The sweep is the union of all translations of M along the straight line [ _Pstart , _Pend ]. In the previous equation, the parameter tε [0,1] plays the role of time. At t = 0, mesh M is translated to position _Pstart , which is written as M + _Pstart . At t = 1, mesh M is translated to position P _end , which is written M + P _end . This is shown in FIG. 13 (in 2D for clarity).

For computational and robust purposes (especially to consider available polylines as opposed to circulating polylines), only the visible portion of M is used by the method (more details later). Provided in). Visible part of M, denoted M ⁺ is the scalar product of the P _{end The} -P _start, the outward normal of M in P, denoted N _P is positive, i.e., <P _{end The} -P _start , N _P >>> 0, the set of points PεM. FIG. 14 shows a 2D example of visible M. Since M ⁺ is created from a straight line segment, the sweep area S (M ⁺ ) is created from adjacent parallelograms as shown in FIG. A 3D version of the triangulated M is shown in FIG. The left figure is M and the right figure is M ⁺ according to _Pstart and _Pend . FIG. 17 shows a sweep of one triangle of M ⁺ . It yields the result of a basic sweep volume, which is the following boundary segment (ie, the outer segment of the volume defined by the integral-sweep over the trajectory of the triangular mesh plane, such boundary segments are As long as it forms a compartmentalization of the entire outer surface of the swept volume, including in any way, eg, defined as all the maximum planes of the outer surface or as its maximum triangle), ie the starting triangle A prism that includes τ _start , an end triangle τ _end , and six side triangles. (Note that the triangular prism is also a Cartesian product with a 1D line that defines the time along the orbit of the triangle, as described in the literature (eg, see Non-Patent Document 19).) It can be seen that the six side triangles are three parallelograms when dealing with a three-axis machining trajectory. The resulting sweep volume S (M ⁺ ) is created from adjacent such triangular prisms, one triangular prism for each triangle of M ⁺ . Note that not all triangles are shown for clarity.

  The method skillfully considers so-called (h, t) diagrams. FIG. 18 shows a straight line segment M (thick straight line) in the yz space that is swept from the initial position to the end position (at a constant speed) according to the trajectory (thick arrow). The M sweep area S (M) is a parallelogram.

The (h, t) diagram associated with dexels (vertical lines) will now be described in detail. The first step (to draw a (h, t) diagram, which does not necessarily have to be performed by the method in practice, as explained above) is that of the dexel line and the sweep area S (M) Calculating the intersection point with the boundary, which generates points P ₁ and P ₂ . From these intersection points, the heights h ₁ and h ₂ , which are the respective abscissas on the dexel line, are obtained. Next, due to the assumption of (for example, constant) speed movement, times t ₁ and t ₂ are calculated accordingly, as shown in FIG. The mathematical operation of the calculation is detailed later.

From now on, the (h, t) diagram associated with Dexel is outlined. It is a 2D view (although for 3D workpieces and tools). Height values h ₁ and h ₂ are reported on the horizontal h-axis, and time values t ₁ and t ₂ are reported on the vertical t-axis. As shown in FIG. 19, this defines a straight line segment connecting the point (h ₁ , t ₁ ) and the point (h ₂ , t ₂ ).

The physical representation is as follows. When time t <t ₁ , the dexel straight line does not meet the moving straight line segment M. When time t = t ₁ , the lower vertex of the straight line meets the dexel straight line at height h ₁ . From time t = t ₁ to time t = t ₂ , the intersection between the straight dexel and the moving straight segment M is a point that moves from P ₁ to P ₂ along the straight dexel. The dependency between t and h is linear. If t> t ₂ , the dexel no longer meets the moving line segment M.

  For clarity, the following description is described in detail using a two-dimensional workpiece and tool. Consider now the 2D workpiece, tool, track, and dexel shown in FIG.

The very first step is to calculate the initial workpiece section, which is the intersection between the dexel line and the workpiece. This produces a value h ₀ and a value h ₉ as shown in FIG. Depending on the shape of the workpiece, the intersection with Dexel includes several sections. Next, the swept volume of the non-blade portion of the tool is calculated and its intersection with the dexel line produces t ₁ , t ₂ , h ₁ , h ₂ as shown in FIG. Next, the sweep volume of the first blade of the tool is calculated and its intersection with the dexel line produces t ₃ , t ₄ , h ₃ , h ₄ as shown in FIG. Next, the sweep volume of the second blade of the tool is calculated and its intersection with the dexel line produces t ₅ , t ₆ , h ₅ , h ₆ as shown in FIG. Next, the sweep volume of the third cutting edge of the tool is calculated and its intersection with the dexel line produces t ₇ , t ₈ , h ₇ , h ₈ as shown in FIG.

All of the previous calculations of height and time are now collected in the (h, t) diagram of dexel D, as shown in FIG. The [h ₀ , h ₉ ] line segment is a so-called workpiece section, which is the intersection between the dexel line and the workpiece. It is represented on the h axis. The (h, t) diagram captures temporal and spatial information so that accurate collision diagnosis can be performed.

  The (h, t) diagram includes a set of non-vertical line segments labeled “cut” or “collision”. The collision diagnosis (S30) is performed as follows. Draw a vertical line in the t direction from all points in the workpiece section. If each such straight line meets the cutting straight line before the collision straight line, there is no collision. If not, there is a collision. In the example, since the cutting straight lines 2 and 3 are arranged below the collision straight line with respect to the t direction, there is no collision as expected.

  The properties referred to earlier in the (h, t) diagram, which provide the simplicity and robustness of the collision diagnosis of the method of the present invention will now be described.

  Depending on the configuration, the (h, t) diagram is labeled by “cutting” or “collision” (the trajectory excludes the point trajectory—ie, PSStart ≠ PEnd—is a rigid body motion. ) Includes a set of non-vertical line segments. These straight line segments are characterized by beneficial properties for accelerating calculations. First, the two straight lines cannot intersect at the internal points, unlike the one shown in FIG. Second, the two straight line segments cannot share end points and overlap, unlike that shown in FIG. This is because the inside of a blade part and the inside of a non-blade part cannot be arrange | positioned at the same place at the same time.

  As a result, each line segment in (h, t) is a mathematical map.

Can be arranged as a set of cutting polylines and collision polylines (more precisely as a graph of such piecewise linear maps). Furthermore, any two polylines cannot intersect at an interior point.

If so, the definition that L _i (h) = + ∞ facilitates the minimum value calculation in the following.

  2D example is a cutting polyline

And cutting polyline

And collision polyline

And play a central role.

  An example of S30 (calculating collision diagnosis) will now be described. This example is just one possible implementation, and the general idea of this example can be implemented in other ways.

  From the viewpoint of calculation, the collision diagnosis of a given dexel D is executed as follows in the example. Polyline

And given the union B of all workpiece sections in dexel D, the first step is

Is a list h ₁ ≦ h ₂ ≦... ≦ h _2n . The ordered list must be understood that those were combined and abscissa h _j collision polylines and abscissa h _j of cutting polyline. The second step is to identify all collision intervals [h _j , h _{j + 1} ] according to the type of lower polyline defined above them. The next algorithm calculates the collision set C as the union of all collision intervals [h _j , h _{j + 1} ].

C: = φ
For j: = 1 to 2n-1 do begin

Find k∈ (1,..., N) such that L _k (m) = min {L _i (m), i = 1,..., N} If the type of polyline L _k is “collision” then
C: = C∪ [h _j , h _{j + 1} ]
End if
End for
A collision occurs only if the workpiece set B meets the collision set C, ie, C∩B ≠ φ. This means that the material of the workpiece meets the non-blade of the tool along the dexel before the blade of the tool.

  Figure 29 shows three polylines

Shows the algorithm. The sorted list of abscissas h _j , i = 1,.

It is. The resulting collision set is

It is. For example, section

Is

And because L ₂ is a collision polyline, it is a collision zone. The workpiece set is not shown.

Returning to the 2D example, the collision set does not meet the workpiece section B = [h ₀ , h ₉ ], C = [h ₆ , h ₂ ], so there is no collision along the dexel.

  A summary of the (at least conceptual) scheme followed by the method is described below (note once again that the method only computes only the polyline endpoints).

  The tool includes adjacent blade portions and non-blade portions. Each part is modeled by a triangulated closed boundary called a “mesh”. The workpiece is modeled by a tridexel structure. An object sweep is a union of copies of an object translated along a trajectory. The basic step of the tool path is the movement of the tool between two consecutive positions. Without loss of generality, the method assumes that the time varies linearly between two consecutive tool positions, the start point is a time equal to 0 and the end point is a time equal to 1. While calculating the intersection between the dexel and the tool sweep, the method also calculates the time at which each tool mesh intersects the dexel. By sorting the result set of times, the method determines every place where it first encounters a material section where the tool part is kept on the dexel (recall that the material section represents a workpiece material). It is possible. If the non-blade first encounters the material, no collision is reported.

  The main feature of the method in the example is to calculate the time of intersection with the dexel by using exclusively the geometry of the swept volume. This information is collected in a so-called (h, t) diagram. This results in increased speed, improved reliability, and increased generality. Refinement of each basic trajectory step is not required, thus allowing good speed performance. Reliability does not depend on any numerical precision value. Performance and reliability are independent of the direction of the displacement vector. Generality: The only assumptions made for the input mesh are verified in most cases because these meshes should approach the boundaries of real 3D solids. Many existing algorithms can be used as preprocessors to repair these meshes if needed.

More specifically, in the example, the step S20 of calculating all polyline endpoints (eg, referred to above as L ₁ , L ₂ , L ₃ ) is performed for each mesh M and for each polyline. For the endpoints, based on all the mesh segments associated with each polyline, the volume S (τ that is swept by the mesh segments according to the trajectory of the cutting tool whose intersection with that of the dexel line corresponds to the endpoints ) Includes a sub-step (referred to as S282). Thanks to the definition of the (h, t) figure and the definition of the polyline that forms it, and thanks to the 3D geometric theory, the end points of the polyline are the support lines (of each dexel) and the faces of each mesh. Corresponds to the intersection with the outer boundary of the volume swept by one of the minutes. With reference to the description regarding FIG. 17, the “boundary surface portion” of the volume S (τ) swept by the mesh surface portion will be described. The method determines such interface segments among all potential interface segments (note that not all such interface segments need necessarily be calculated). Next, the example calculating step S20 determines each endpoint (with respect to the retained scale) based on such a (geometric) intersection between the dexel line and the determined interface segment. It includes a sub-step (referred to as S284) that calculates a set time and height. This allows a simple calculating step S20. In fact, this time calculation comes directly from geometric considerations, as time and height change linearly as long as the 3D intersection is kept within the same triangular prism.

  This method of calculating the “h” parameter through a 3D line / triangle intersection will now be further detailed in the examples.

  triangle

And straight line

think of. The goal is to test whether the line intersects the triangle and, if so, to calculate the coordinates of the intersection in the dexel frame. In particular, these coordinates include (or at least provide) a height above D.

Let Q be a plane orthogonal to D and d be the intersection of D and Q. Note that xyz is the reference axis coordinate system, where D is parallel to the z-axis (representing height), Q is the xy plane and D (representing the dexel grid support plane). It is defined by two coordinates (x _D , y _D ) in the plane xy. If D is parallel to the y axis, Q is the zx plane, and D is defined by two coordinates (z _D , x _D ) in the plane zx. If D is parallel to the x-axis, Q is the yz plane, and D is defined by two coordinates (y _D , z _D ) in the plane yz.

  Let U, V, and W be the vertices of the triangle Δ, and let U ′, V ′, and W ′ be the respective projections on the plane Q that define the 2D triangle Δ ′. FIG. 31 shows the geometry when D is parallel to the z-axis.

  It is well known from the state of the art that the straight line D meets the triangle Δ only when the point d is inside the triangle Δ ′. Only if all three algebraic areas Area (d, V ′, W ′), Area (U ′, d, W ′), and Area (U ′, V ′, d) have the same sign. , Point d is inside the triangle Δ ′. Furthermore, the height h of the intersection D∩Δ is:

Where h _u , h _v , and h _w are the heights of points U, V, and W along the straight line D, respectively.

Finally, the 3D coordinates of the point D∩Δ are known by combining the 2D coordinates of D in the plane Q together with h. If D is parallel to the z axis, then D∩Δ = (x _D , y _D , h). When D is parallel to the y-axis, D∩Δ = (x _D , h, z _D ). When D is parallel to the x-axis, D∩Δ = (h, y _D , z _D ).

  This method of calculating the “t” parameter will now be described in an example.

  triangle

But

From

Consider the situation in which a translation is made. Let T be the corresponding sweep volume (which is a non-degenerate triangular prism).

Let A, B, and C be the vertices of the triangle τ, e ₁ = B−A, e ₂ = C−A, and e ₃ = P _end −P _start . This is illustrated in FIG. Let τ _start = τ + P _{start be} the initial copy of triangle τ, and τ _end = τ + P _{end be} the final copy of triangle τ. Since the triangle τ is not degenerated, the vector e ₁ and the vector e ₂ are not on the same line. Since the triangle τ is not translated along its support plane, the vector e ₃ does not belong to the plane stretched by e ₁ and e ₂ . This makes the matrix [e ₁ e ₂ e ₃ ] reversible. As a result, an arbitrary point PεT is given by three numbers r, s, t
P = A + re ₁ + se ₂ + te ₃
It is expressed uniquely as follows.

Note that the vectors e ₁ , e ₂ , e ₃ are not normalized and they are not orthogonal to each other.

  Given the coordinates of the point P, the numbers r, s, and t are linear simultaneous equations.

Can be calculated by solving

The number t plays the role of time as the triangle τ moves from P _start to P _end . If t = 0, the point P belongs to τ _start , and if t = 1, the point P belongs to τ _end , and if 0 <t <1, the point P is the intermediate triangle τ + (tP _end + (1-t) _Pstart ).

  The generalization of 3D geometry to (h, t) diagrams will now be described.

The triangular prism includes two triangles (τ _start and τ _end ) and three plane parallelograms. The parallelogram is triangulated so that the triangular prism T includes six side triangles in addition to τ _start and τ _end . Given such a triangulated triangular prism and dexel straight line D, calculating D∩T becomes a problem of line / triangle intersection, as explained in the previous paragraph. Let P∈D∩T. The h parameter is calculated using equation (1) and the t parameter is calculated using equation (2). If P belongs to τ _start , the t parameter is t = 0. If P belongs to τ _end , the t parameter is t = 1.

  The data structure is, for example, the same number of (h, t) parameters as dexel D and that there are points in D∩T and that there is a triangular prism T characterized by non-empty intersection with D. Associate. In the example, only the endpoints of the polyline are retained or even calculated first.

FIG. 33 shows D∩T = {P ₁ , P ₂ }, where P ₁ ∈τ _start , ie t ₁ = 0, and P ₂ belongs to the side triangle, ie 0 <T ₂ <1. The data structure associates (h ₁ , t ₁ ) and (h ₂ , t ₂ ) with dexel D. FIG. 34 shows D∩T = {P ₁ , P ₂ }, where P ₁ and P ₂ belong to the side triangles, that is, 0 <t ₁ <1, 0 <t ₂ <1. It is. The data structure associates (h ₁ , t ₁ ) and (h ₂ , t ₂ ) with dexel D.

  The generalization of the exemplary calculations designed with reference to FIGS. 31-34 to a 5-axis trajectory will now be described.

  The method for a basic trajectory defined by translation can be generalized to a basic trajectory defined by rigid body motion including rotation. This is even more so if the angle value of rotation is sufficiently small. The following describes how the (h, t) parameter is calculated in this situation.

Let τ _start and τ _{end be} the initial triangle and the end triangle of the basic trajectory. The boundary of the swept volume is approximated by six side triangles along with triangles τ _start and τ _end . The three line segments that connect the vertices of τ _start with their respective copies in τ _end are called “time line segments”, as shown in FIG. Next, the approximate swept volume is divided into three tetrahedra. One of them includes τ _start and the other includes τ _end . Each tetrahedron contains only one time line segment, as shown in FIG. The vectors e ₁ , e ₂ , e ₃ are associated with each tetrahedron according to the following strategy. The vector e ₃ is a time line segment, and the vectors e ₁ and e ₂ are the sides of τ _start and / or τ _end associated with e ₃ . FIG. 37 shows the e ₁ , e ₂ , and e ₃ vectors of each tetrahedron.

  The calculation of the (h, t) parameter is performed by intersecting the linear dexel with each boundary surface portion of each tetrahedron and using equations (1) and (2). The polylines in the (h, t) diagram are generated accordingly.

  The above description provides general details about the method aspects, details about the general intuition behind the method (ie, the (h, t) diagram), and (eg, in particular one dexel and one triangular prism). Provides examples of some calculations performed by the method to obtain the endpoints of a polyline via a geometric intersection (which details the intersection between and). However, real-world machining simulations involve a huge number of dexels and triangles, making computation time a serious problem. The following is about how the dexels are arranged and how the topological adjacency of the triangular prism (caused by sweeping adjacent triangles) is used to accelerate the calculation An example of the method will be described.

In this example, the step S20 of calculating the end points of all the polylines (L ₁ , L ₂ , L ₃ etc.) for each mesh M first determines the visible part (M ⁺ ) of the mesh (M) ( A sub-step) (referred to as S22). The visible portion is the portion of the mesh (eg, the smallest subset of surface segments) that is directed toward the cutting tool trajectory, as described with reference to FIGS. Note that M ⁺ includes several sub-mesh (ie, separate sub-mesh, each consisting of connected surface segments). This is done in any way. Next, step S20 of calculating, in accordance with the trajectory of the cutting tool (called S24) to calculate the (called .differential.S (M ⁺⁾⁾ boundary of the volume that is swept by the visible portion (S (M ⁺⁾⁾ sub Includes steps. This is performed using triangular prisms and / or tetrahedrons as described above. And then the calculating step S20 comprises, for each end of each polyline (calculated), the determining sub-step referred to above referred to as S282 and the calculating sub-step referred to above referred to as S284. Including an iteration sub-step (referred to as S28). Sub-step S282 for determining the boundary segment consists of identifying each boundary segment of the calculated boundary ∂ S (M ⁺ ) of the volume (S (M ⁺ )) swept by the visible portion. Actually, depending on the configuration, the end point of the polyline in the (h, t) diagram is not the boundary surface portion of the dexel straight line and the volume surface swept by the mesh surface portion, but an arbitrary boundary surface portion S (M ⁺ ) Corresponds to the fellowship with those forming. Thus, the example method takes advantage of the geometric characteristics of interest to improve efficiency.

  The example calculating step S20 further includes (obviously) a sub-step S26 that determines adjacency information for each mesh M with respect to the volume swept by the face portion of the visible portion. This information is any type of information that indicates which volumes (eg, triangular prisms and / or tetrahedrons) swept by a surface segment are adjacent. This is done in a simple manner based on the topology of the mesh and on the adjacency and / or connectivity information of the faces in the mesh. This topology information nevertheless allows great speed efficiency.

In fact, for each respective polyline, the next calculating step S20 consists of the “first” (or “entrance”) face segment of the calculated boundary ∂S (M ⁺ ) and the calculated boundary ∂S. It includes a sub-step S282 in which the “second” (or “exit”) face segment of (M ⁺ ) is determined in a different way. Each polyline end generally corresponds by definition to two 3D points (ie, those at the intersection between the same dexel line and the two elements of the calculated boundary ∂S (M ⁺ )). Now, in an iterative sub-step S28 performed in the example, the method pairs such boundary surface segments (ie, the “first surface segment” where the dexel line enters the sweep volume, for example, and the dexel line From the swept volume, for example, the “second area” that emerges). The ordering ("first" and "second", "enter" and "exit") is purely arbitrary and depends on the implementation.

The problem is that instead of forcibly identifying all such surface segments, each time the method determines / finds the first surface segment, the associated surface segment (ie, “second surface” To find the “minute”), so-called “topological propagation”. Specifically, the sub-step S282 for determining the boundary portion of the volume S (τ) associated with the end point of the polyline is described above with reference to geometric calculations (and thus with reference to FIGS. 31-37). Determining the first surface segment of the calculated boundary ∂S (M ⁺ ) intersected by the dexel straight line (by a normal 3D intersection and a relatively heavy calculation, such as a first calculation step). . However, in the alternation between the recurring substeps S28, the substep S282 for determining the boundary portion of the volume S (τ) associated with the other endpoint of the same polyline is based on the adjacency information (and thus relative Topological propagation (in a very fast way), the second area of the computed boundary ∂S (M ⁺ ) intersected by the dexel straight line (in other words, the dexel straight line is Determining the surface segment associated with the first surface portion of the pair, thus intersecting ∂S (M ⁺ ), possibly in two or more such pairs or instances thereof Consists of.

  This topological propagation feature will now be further detailed.

The step of calculating the dexel-triangle intersection is performed in the example as follows. Let M be the initial mesh and let P _start and P _{end be} the start and end points of the basic trajectory, respectively. The M ^+, as a part of M, which is directed towards the base track, the E ^+, the M ⁺ of the boundary. Without loss of generality, assume that M ⁺ is a connected set. In essence, E ⁺ is a three-dimensional closed polyline. FIG. 38 illustrates the situation.

Now, consider the direction V = P _end -P _start along the M ⁺ sweep volume S (M ^+). Boundary of S (M ⁺⁾ is referred to as the ∂S (M ^+). In practice, S (M ⁺ ) is created from adjacent triangular prisms and is characterized by the following characteristics:
● Each triangular prism p _i is an extrusion of an M ⁺ triangle τ _i .
● The boundary ∂ S (M ⁺ ) of S (M ⁺ ) is
□ containing triangle M ⁺ in triangular □ end position P _{end The} of M ⁺ in the parallelogram □ initial position P _start extruded from E ⁺ sides.
The parallelogram shared by two adjacent triangular prisms p _i and p _j is an extrusion of the side shared by M ⁺ triangles τ _i and τ _j .

These adjacency characteristics are captured through an appropriate topology data structure. They are used intensively by the propagation algorithm. The first step is to calculate the intersection between D and ∂S (M ⁺ ). The surface segment f ₀ ε∂S (M ⁺ ) where the intersection occurs starts topological propagation. Next, the next triangular prism of S (M ⁺ ) intersected with D is found by visiting the neighborhood of f ₀ . This is performed between label A and label B in the diagram of FIG.

Propagation ends when a point on the boundary of S (M ⁺ ) is calculated. The algorithm continues by searching for another intersection between D and the boundary portion of S (M ⁺ ), as in the general case where M ⁺ is not a connected set. Note that according to this propagation method, the h values calculated from the intersections are sorted quite naturally, which improves efficiency. This property is used to construct the (h, t) diagram (ie, without any sort on the h values).

From the following, the core of topological propagation is explained. It is performed between label A and label B in the diagram of FIG. Primarily, to bounded surface region f _0, or produce a surface region f _0, is identified bounded sides l _0, appropriate triangles associated with l ₀ or f ₀ τ∈M ⁺ also identified. The next triangular prism was created by the triangle τ. The process relies on a natural parallelogram-versus-triangle of surface area f ₀ as illustrated in the diagram of FIG.

The algorithm is illustrated in the situation shown in FIG.
1. An intersection between D and ∂S (M ⁺ ) occurs at the surface segment f ₀ .
2. Since the surface segment f ₀ is a parallelogram, the boundary side l ₀ ∈E ⁺ that generated the boundary surface segment f ₀ is acquired.
3. Get a unique triangle τ ₁ bounded by l ₀ .
4). Calculate the other intersection between D and the surface area of extrusion p ₁ of τ ₁ .
5). The side l ₁ that starts the surface segment f ₁ of p ₁ that intersects D is acquired.
6). Obtain a triangle τ ₂ that shares τ ₁ and l ₁ .
7). Calculate the other intersection between D and the surface area of the extrusion p ₂ of τ ₂ .
8). The side l ₂ that starts the surface segment f ₂ of p ₂ that intersects D is acquired.
9. Obtain a triangle τ ₃ sharing τ ₂ and l ₂ .
10. Calculate the other intersection between D and the surface area of the extrusion p ₃ of τ ₃ .
11. An edge l ₃ starting with a surface segment f ₃ of p ₃ intersecting with D is acquired.
12 The side l ₃ is the boundary side of M ⁺ , and therefore f ₃ is the boundary surface of S (M ⁺ ), and the dexel D comes out of S (M ⁺ ) locally, so the propagation ends.

The algorithm is illustrated in another situation. The left diagram in FIG. 42 shows a situation where the surface segment f ₀ intersecting with the dexel D is a triangle. The right diagram of FIG. 42 shows S (M ⁺ ) seen from the viewpoint defined by V = P _end −P _start . In the right figure, each triangle is a bottom surface of a triangular prism orthogonal to the view plane.
1. An intersection between D and ∂S (M ⁺ ) occurs at the surface segment f ₀ .
2. The surface segment f ₀ is a triangle, and the side l ₀ is to generate a parallelogram intersecting D. Compute the intersection between D and this parallelogram.
3. Get a unique triangle τ ₁ that shares f ₀ and l ₀ .
4). Calculate the other intersection between D and the surface area of extrusion p ₁ of τ ₁ .
5). The side l ₁ that starts the surface segment f ₁ of p ₁ that intersects D is acquired.
6). Obtain a triangle τ ₂ that shares τ ₁ and l ₁ .
7). Calculate the other intersection between D and the surface area of the extrusion p ₂ of τ ₂ .

The area f ₂ of p ₂ intersecting with D is the boundary area of S (M ⁺ ), and therefore the dexel D comes out of S (M ⁺ ) locally, so the propagation ends.

Here, as a further improvement, the sub-step S282 of determining the first surface segment performs rasterization over the set of dexels. In other words, the sub-step S282 of determining the first surface segment is provided by rasterizing all elements of ∂S (M ⁺ ) across dexels that are considered elements of the 2D grid. A dexel is considered an element of a 2D grid (in a plane orthogonal to the grid, a dexel is a 2D position that is compared to a pixel).

  The dexels in the x, y, and z directions are arranged in adjacent rectangular groups of nm dexels. Implementation shows that n = m = 8 gives good performance. Each dexel group is associated with its bounding box. Searching which dexels meet a given triangular prism is filtered by first excluding the group of dexels whose bounding box does not meet the triangular prism.

  It should be noted that the above example does not limit the scope of the method of the present invention, as obvious modifications are also contemplated. In particular, the above description has always presented a “clean” 3D intersection (between the dexel line and the interface segment, where the intersection was always considered a 3D position). However, if a dexel line intersects with a boundary segment to form an intersection line / straight line (not a point), the dexel does not intersect with one boundary segment and several boundary segments and the boundary between them All obvious fits for extreme cases are contemplated by the method of the present invention, including the case of crossing (in a straight line between two segments or even in a point between, for example, three or more segments). It will be understood that The method addresses these degenerate cases, for example by relying on so-called exact predicates (see Non-Patent Document 20), which guarantees robustness and efficiency. All specific obvious implementations are also contemplated by the method, such as handling dexel lines that intersect the same interface multiple times (eg, due to a specific trajectory).

Claims (12)

A computer-implemented method for simulating machining of a workpiece using a cutting tool having at least one cutting portion and at least one non-cutting portion, comprising:
A set of dexels representing the workpiece, each dexel comprising a set of at least one segment representing an intersection between a line and the workpiece; and
The trajectory of the cutting tool, which is a precise movement;
Providing a set (S10) of meshes (M), each of which represents a respective cutting or non-cutting part of the cutting tool;
For each dexel (D)
All polylines (L ₁ , L ₂ , L) describing the time of intersection (t) between the line of the dexel (D) and the mesh as a function of the height of intersection (h) according to the trajectory of the cutting tool ₃ ) calculating an end point of each mesh (M) (S20);
Testing a collision between the cutting tool and the workpiece along the dexel (S30), wherein the test is a height value corresponding to a position belonging to a lower envelope of a set of all polylines of all meshes. And determining whether the polyline belonging to the position is associated with a non-cutting portion, the height value belonging to the dexel line segment, the testing step (S30). A computer-implemented method characterized by the above. The step (S20) of calculating the end points of all the polylines (L ₁ , L ₂ , L ₃ ) is performed for each mesh (M) and for each end point of each polyline.
Swept by the surface of the mesh according to the trajectory of the cutting tool, with the intersection of the lines of the dexels corresponding to the end points, based on all the surfaces of the mesh associated with the respective polylines Determining a boundary surface of the volume (S (τ)) (S282);
The computer-implemented method of claim 1, further comprising: calculating time and height based on an intersection between the line of the dexel and the determined boundary surface (S284). The step (S20) of calculating the end points of all the polylines (L ₁ , L ₂ , L ₃ ) is performed for each mesh (M):
Determining the visible portion of the mesh (M ⁺ ) (S22), wherein the visible portion is the portion of the mesh that is directed toward the trajectory of the cutting tool (S22);
Calculating a boundary (∂S (M ⁺ )) of a volume ° (S (M ⁺ )) swept by the visible portion according to the trajectory of the cutting tool (S24);
The step of determining the boundary surface of the volume ° (S (τ)) swept by the face of the mesh with the intersection of the line of the dexel corresponding to the end point (S282) and calculating the time and height The step (S284) of repeating the step (S284) for each end point of each polyline, the step (S282) of determining the boundary surface is a volume (S (M ⁺⁾ wherein each composed of identifying the interface of the computed boundary (.differential.S (M ^{+)) of),} according to, further comprising a step (28) for performing return該繰Item 3. A computer-implemented method according to Item 2. The step (S20) of calculating the end points of all the polylines (L ₁ , L ₂ , L ₃ ) determines, for each mesh (M), adjacent information with respect to the volume swept by the surface of the visible part ( S26) and for each polyline:
Said step (S282) of determining a boundary surface of the volume (S (τ)) swept by the surface of the mesh with the intersection of the line of the dexel corresponding to the first end point of the polyline; Determining a first surface of the calculated boundary (∂S (M ⁺ )) of the volume (S (M ⁺ )) swept by the visible part by geometric calculation, Determining (S282) that the plane of is intersected by the line of the dexel;
Determining the boundary surface of the volume swept by the surface (S (τ)) with the intersection of the line of the dexel corresponding to the second endpoint of the polyline, the step (S282), Determining the second face of the calculated boundary (∂S (M ⁺ )) of the volume (S (M ⁺ )) swept by the visible part by topology propagation based on the neighbor information, The computer-implemented method of claim 3, further comprising the step of determining (S282) that a second surface is intersected by the line of the dexels.   5. The computer-implemented method of claim 4, wherein the repetitive step (28) is parallelized on the set of dexels.   The computer-implemented method of claim 5, wherein determining (282) the first surface comprises performing rasterization on the set of dexels.   A method for producing a product, the method comprising repeating the method for simulating machining according to any of claims 1 to 6, and thereby performing a machining phase on a workpiece. Including a simulation phase.   7. A data structure comprising simulation specifications for machining a workpiece using a cutting tool having at least one cutting portion and at least one non-cutting portion, corresponding to the method of any of claims 1-6.   A system comprising a processor coupled to a memory having instructions recorded thereon for performing the method of any of claims 1-6.   The system of claim 9, wherein the processor is a graphical processing unit.   A computer program comprising instructions for executing the method of any of claims 1-6.   A computer-readable storage medium on which the computer program of claim 11 is recorded.

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